/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x y)
(RULES
-(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(-(x,y),-(x,y))
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))

Problem 1: 

SCC Processor:
-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(-(x,y),-(x,y))
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(-(x,y),-(x,y))
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
->->-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(-(x,y),-(x,y))
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
-> Usable rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[-](X1,X2) = 2.X1
[neg](X) = 2.X + 2
[-#](X1,X2) = 2.X1

Problem 1: 

SCC Processor:
-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
->->-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))

Problem 1: 

Subterm Processor:
-> Pairs:
 -#(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -#(x,y)
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
->Projection:
 pi(-#) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 -(-(neg(x),neg(x)),-(neg(y),neg(y))) -> -(-(x,y),-(x,y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.